Our concern is the numerical identification of traffic flow parameters in a macroscopic one-dimensional model whose governing equation is strongly degenerate parabolic. The unknown parameters determine the flux and the diffusion terms. The parameters are estimated by repeatedly solving the corresponding direct problem under variation of the parameter values, starting from an initial guess, with the aim of minimizing the distance between a time-dependent observation and the corresponding numerical solution. The direct problem is solved by a modification of a well-known monotone finite difference scheme obtained by discretizing the nonlinear diffusive term by a formula that involves a discrete mollification operator. The mollified scheme occupies a larger stencil but converges under a less restrictive Courant-Friedrichs-Lewy (CFL) condition, which allows one to employ a larger time step. The ability of the proposed procedure for the identification of traffic flow parameters is illustrated by a numerical experiment.